Woods and McIlroy made honorary members by R&A Golf Club of St Andrews
American Woods, a 15-times major champion, is bidding to win the Open for the fourth time this week at St Andrews to add to his victories in 2000, 2005 and 2006.
"I am grateful for this invitation to become an Honorary Member of The Royal and Ancient Golf Club of St Andrews.
"It is not only the home of golf but a place in this world that I hold near my heart."
Northern Ireland's McIlroy won the Open at Royal Liverpool in 2014, one of his four major titles.
"It's a privilege to represent a club that has done so much for golf over so many years and I'm proud to play my part in promoting golf around the world," he said.
Scotland's Lawrie, who won the 1999 Open, will have the honour of striking the first tee shot of the 150th Open on Thursday.